The total quasi-steady-state for multiple alternative substrate reactions

The Michaelis–Menten–Briggs–Haldane approximation and its extension, the total quasi-steady-state approximation (tQSSA) are famous assumptions for simplification of mathematical modeling of enzyme-substrate reactions. These approximations and their validity conditions are well studied for a single s...

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Bibliographic Details
Published in:Journal of mathematical chemistry 2022-05, Vol.60 (5), p.841-861
Main Authors: Besya, Azimberdy, Rao, Shodhan
Format: Article
Language:English
Subjects:
Approximation
Chemistry
Chemistry and Materials Science
Exact solutions
Math. Applications in Chemistry
Mathematical analysis
Original Paper
Perturbation methods
Physical Chemistry
Singular perturbation
Steady state
Substrates
Theoretical and Computational Chemistry
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Summary:The Michaelis–Menten–Briggs–Haldane approximation and its extension, the total quasi-steady-state approximation (tQSSA) are famous assumptions for simplification of mathematical modeling of enzyme-substrate reactions. These approximations and their validity conditions are well studied for a single substrate reaction system. However, the extension of these studies for the tQSSA of the general case of multiple substrate reactions is yet to be performed precisely due to the consequent non-linear expressions for tQSSA. In this paper, we introduce a linearization method for equations governing the tQSSA of multiple substrate reactions to obtain an analytical solution for the evolution of concentrations of reactants that is valid throughout the whole time period. In addition, we provide the validity conditions of the tQSSA for multiple substrate reaction systems using the singular perturbation analysis method.
ISSN:0259-9791
1572-8897
DOI:10.1007/s10910-022-01339-6